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Date:         Thu, 14 Sep 2000 15:37:26 GMT
Reply-To:     z <gzuckier@MY-DEJA.COM>
Sender:       "SAS(r) Discussion" <SAS-L@LISTSERV.UGA.EDU>
From:         z <gzuckier@MY-DEJA.COM>
Organization: - Before you buy.
Subject:      Why offset in confidence interval for proportions?

Hi. This is more a stats question than a SAS one, but.... I'm trying to wade through the JCAHO ORYX reporting requirements. Their formulae for upper and lower limits for a 99% confidence interval for a proportion are U=((p+(Z^2)/(2n))+Z(root))/(1+(Z^2)/n) L=((p+(Z^2)/(2n))-Z(root))/(1+(Z^2)/n) where root=((z^2)/(4(n^2))+p(1-p)/n)^.5 Z=2.576 n=Number of patients p=observed proportion

I can't exactly see where this comes from (I would have come up with p(+or-)Z(p(1-p)/n)^.5 myself), and more to the point, this gives me a confidence interval whose center is offset from p by the (Z^2)/2n term. Waiting for the JCAHO to clarify is a slow process, in the meantime, can anyone explain the theory behind this calculation? Thanks.

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